Discussion:
tensor symbol
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mrlinux
2004-10-21 15:55:10 UTC
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Hi,

How can I get the tensor symbol, I mean the doublearrow over \epsilon ???


thanks in advance
José Carlos Santos
2004-10-21 16:23:43 UTC
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Post by mrlinux
How can I get the tensor symbol, I mean the doublearrow over \epsilon ???
I dont't think that I've ever seen that symbol, but you can obtain
it with $\stackrel{\Rightarrow}{\epsilon}$. I hope not to have
misunderstood what you mean by doublearrow.

Best regards,

Jose Carlos Santos
Michele Dondi
2004-10-21 21:58:30 UTC
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Post by mrlinux
How can I get the tensor symbol, I mean the doublearrow over \epsilon ???
Are you sure that is "*the* tensor symbol"? I've never ever seen it in
print or in handwriting either...


Just curious,
Michele
--
{$_=pack'B8'x25,unpack'A8'x32,$a^=sub{pop^pop}->(map substr
(($a||=join'',map--$|x$_,(unpack'w',unpack'u','G^<R<Y]*YB='
.'KYU;*EVH[.FHF2W+#"\Z*5TI/ER<Z`S(G.DZZ9OX0Z')=~/./g)x2,$_,
256),7,249);s/[^\w,]/ /g;$ \=/^J/?$/:"\r";print,redo}#JAPH,
Harald Harders
2004-10-21 22:00:43 UTC
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Post by Michele Dondi
Post by mrlinux
How can I get the tensor symbol, I mean the doublearrow over \epsilon ???
Are you sure that is "*the* tensor symbol"? I've never ever seen it in
print or in handwriting either...
And what exactly is a tensor? A scalar, a vector, ... Do you use the
same symbol for all stages/orders (what is the correct term in English)?

Harald
--
Harald Harders
***@tu-bs.de
http://www.harald-harders.de
Gregory L. Hansen
2004-10-22 16:38:31 UTC
Permalink
Post by Harald Harders
Post by Michele Dondi
Post by mrlinux
How can I get the tensor symbol, I mean the doublearrow over \epsilon ???
Are you sure that is "*the* tensor symbol"? I've never ever seen it in
print or in handwriting either...
And what exactly is a tensor? A scalar, a vector, ... Do you use the
same symbol for all stages/orders (what is the correct term in English)?
Usually the word tensor is used for something with at least two indices.
Scalars and vectors may be tensors, but they already have their own names.
So if someone mentions, e.g., a tensor force, you can be sure that he
doesn't mean a zeroeth-rank tensor force or a first-rank tensor force.

I've seen double arrows used for two-index tensors (a vector has one index
and one arrow head, a 2nd rank tensor has two indices and two arrow
heads). Also an underline, two underlines, a different font, no
particular markings but the tensor status implied from context, and
notations like (A_uv), parentheses or brackets indicating the whole thing
and not just a component.
--
"Very well, he replied, I allow you cow's dung in place of human
excrement; bake your bread on that." -- Ezekiel 4:15
Harald Harders
2004-10-22 18:47:04 UTC
Permalink
Post by Gregory L. Hansen
Post by Harald Harders
Post by Michele Dondi
Post by mrlinux
How can I get the tensor symbol, I mean the doublearrow over \epsilon ???
Are you sure that is "*the* tensor symbol"? I've never ever seen it in
print or in handwriting either...
And what exactly is a tensor? A scalar, a vector, ... Do you use the
same symbol for all stages/orders (what is the correct term in English)?
Usually the word tensor is used for something with at least two indices.
Scalars and vectors may be tensors, but they already have their own names.
So if someone mentions, e.g., a tensor force, you can be sure that he
doesn't mean a zeroeth-rank tensor force or a first-rank tensor force.
Ah, I know what a tensor is. But what I ment is that you should not use
the same symbol for all orders. I have learned a nomenclature for tensors
at university that uses simple underline for vectors, double underline
for second-rank tensors and a tilde under the symbol with the rank of
the tensor below it for higher-rank tensors, for example Hooke's law:

s = C .. e
= ~ =
4

(of course with a smaller 4 under the C). And of course, there is the
index notation:

s_ij = C_ijkl e_kl

But for a single tensor, the index notations gives one component instead
of the whole tensor. And (s_ij) is the component matrix for a given
coordinate system, still not the whole tensor because you have to give
the coordinate system(s) to get the tensor itself.

Harald
--
Harald Harders
***@tu-bs.de
http://www.harald-harders.de
Gregory L. Hansen
2004-10-22 19:54:03 UTC
Permalink
Post by Harald Harders
Post by Gregory L. Hansen
Post by Harald Harders
Post by Michele Dondi
Post by mrlinux
How can I get the tensor symbol, I mean the doublearrow over \epsilon ???
Are you sure that is "*the* tensor symbol"? I've never ever seen it in
print or in handwriting either...
And what exactly is a tensor? A scalar, a vector, ... Do you use the
same symbol for all stages/orders (what is the correct term in English)?
Usually the word tensor is used for something with at least two indices.
Scalars and vectors may be tensors, but they already have their own names.
So if someone mentions, e.g., a tensor force, you can be sure that he
doesn't mean a zeroeth-rank tensor force or a first-rank tensor force.
Ah, I know what a tensor is. But what I ment is that you should not use
the same symbol for all orders. I have learned a nomenclature for tensors
at university that uses simple underline for vectors, double underline
for second-rank tensors and a tilde under the symbol with the rank of
s = C .. e
= ~ =
4
(of course with a smaller 4 under the C). And of course, there is the
The tilde notation is new to me, but the underlines have always bugged
me. But I see nothing wrong with a single arrow for a vector, a double
arrow for a second-rank tensor, and a tilde over the symbol with the rank
of the tensor above it for higher-rank tensors. I'd probably be the only
person in the world using that particular convention, though.
Post by Harald Harders
s_ij = C_ijkl e_kl
But for a single tensor, the index notations gives one component instead
of the whole tensor. And (s_ij) is the component matrix for a given
coordinate system, still not the whole tensor because you have to give
the coordinate system(s) to get the tensor itself.
If you're talking about one particular component, then you need to know
the basis for that to make any sense. But when you have all of them
together, it really doesn't matter. s_ij = C_ijkl e_kl no matter what
basis you use. s_11 or s_32 would depend on the basis, but that s_ij is
related to that particular sum doesn't.

Or another example, v_i = g_ij v^j, lowering an index written out as
components, or v = (g_ij) ...

Eh, I guess I don't know of notation that distinguishes a contravariant
from a covariant vector, except for where you put the index. Maybe that's
what underlines are good for.
--
"In any case, don't stress too much--cortisol inhibits muscular
hypertrophy. " -- Eric Dodd
Harald Harders
2004-10-23 01:43:58 UTC
Permalink
Post by Gregory L. Hansen
The tilde notation is new to me, but the underlines have always bugged
me. But I see nothing wrong with a single arrow for a vector, a double
arrow for a second-rank tensor, and a tilde over the symbol with the rank
of the tensor above it for higher-rank tensors. I'd probably be the only
person in the world using that particular convention, though.
Post by Harald Harders
s_ij = C_ijkl e_kl
But for a single tensor, the index notations gives one component instead
of the whole tensor. And (s_ij) is the component matrix for a given
coordinate system, still not the whole tensor because you have to give
the coordinate system(s) to get the tensor itself.
If you're talking about one particular component, then you need to know
the basis for that to make any sense. But when you have all of them
together, it really doesn't matter. s_ij = C_ijkl e_kl no matter what
basis you use. s_11 or s_32 would depend on the basis, but that s_ij is
related to that particular sum doesn't.
Yes, that's clear. But it's really OT.
--
Harald Harders
***@tu-bs.de
http://www.harald-harders.de
Michele Dondi
2004-10-23 06:02:45 UTC
Permalink
Post by Harald Harders
Post by Michele Dondi
Are you sure that is "*the* tensor symbol"? I've never ever seen it in
print or in handwriting either...
And what exactly is a tensor? A scalar, a vector, ... Do you use the
same symbol for all stages/orders (what is the correct term in English)?
I do know what a tensor is (in most contexts it's actually used). For
practical uses I like the Abstract Index Notation. Well, at least I
became very familiar with it when studying on "Wald".

Simply, had never ever seen the double arrow notation...


Michele
--
Post by Harald Harders
It's because the universe was programmed in C++.
No, no, it was programmed in Forth. See Genesis 1:12:
"And the earth brought Forth ..."
- Robert Israel in sci.math, thread "Why numbers?"
Madhusudan Singh
2004-10-21 22:03:09 UTC
Permalink
Post by mrlinux
Hi,
How can I get the tensor symbol, I mean the doublearrow over \epsilon ???
thanks in advance
A tensor is usually written with its indices. This double arrow business is
new.

You can use \stackrel to get what you want, but I am not sure that is a
proper notation for a tensor.
Dan Luecking
2004-10-22 15:59:51 UTC
Permalink
On Thu, 21 Oct 2004 18:03:09 -0400, Madhusudan Singh
Post by Madhusudan Singh
Post by mrlinux
Hi,
How can I get the tensor symbol, I mean the doublearrow over \epsilon ???
thanks in advance
A tensor is usually written with its indices.
One can use a single symbol to represent a tensor in the same way that
one can write a vector or matrix. A vector _is_ a tensor of order one,
a matrix _is_ a tensor of order 2.
Post by Madhusudan Singh
This double arrow business is new.
I admit I've never seen it, but I have seen various special fonts
used.
Post by Madhusudan Singh
You can use \stackrel to get what you want, but I am not sure that is a
proper notation for a tensor.
\stackrel is wrong anyway. It produces a RELation, which gives incorrect
spacing for what should be treated as a variable, and also incorrect
vertical position of the base. Perhaps amsmath.sty with
\vec{\vec{\epsilon}?


Dan
--
Dan Luecking Department of Mathematical Sciences
University of Arkansas Fayetteville, Arkansas 72701
To reply by email, change Look-In-Sig to luecking
Giuseppe Bilotta
2004-10-22 19:46:41 UTC
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Post by Dan Luecking
One can use a single symbol to represent a tensor in the same way that
one can write a vector or matrix. A vector _is_ a tensor of order one,
a matrix _is_ a tensor of order 2.
Well, this is strictly speaking not true (a tensor is an object
with certain properties, and although every rank 2 tensor can
be represented as a matrix, not all matrices are (the
representation of) a tensor). But this is going OT.
Post by Dan Luecking
Post by Madhusudan Singh
This double arrow business is new.
I admit I've never seen it, but I have seen various special fonts
used.
Well, it's not very much used. I've only seen it used once, by
my Physics professor. Everybody else just stuck to use letters
in the whereabouts of T :)
--
Giuseppe "Oblomov" Bilotta

Can't you see
It all makes perfect sense
Expressed in dollar and cents
Pounds shillings and pence
(Roger Waters)
Madhusudan Singh
2004-10-23 03:14:17 UTC
Permalink
Post by Giuseppe Bilotta
Post by Dan Luecking
One can use a single symbol to represent a tensor in the same way that
one can write a vector or matrix. A vector _is_ a tensor of order one,
a matrix _is_ a tensor of order 2.
Well, this is strictly speaking not true (a tensor is an object
with certain properties, and although every rank 2 tensor can
be represented as a matrix, not all matrices are (the
representation of) a tensor). But this is going OT.
Right. Thanks for the correction.
Madhusudan Singh
2004-10-23 03:13:08 UTC
Permalink
Post by Dan Luecking
Post by Madhusudan Singh
A tensor is usually written with its indices.
One can use a single symbol to represent a tensor in the same way that
one can write a vector or matrix. A vector _is_ a tensor of order one,
a matrix _is_ a tensor of order 2.
Of course. I was just making a reference to the widespread use of the
Einstein summation convention.
Post by Dan Luecking
Post by Madhusudan Singh
This double arrow business is new.
I admit I've never seen it, but I have seen various special fonts
used.
I have seen a bold-faced letter with a bold tilde on top a few times. Once
even a bold faced cursive capital letter.
Post by Dan Luecking
Post by Madhusudan Singh
You can use \stackrel to get what you want, but I am not sure that is a
proper notation for a tensor.
\stackrel is wrong anyway. It produces a RELation, which gives incorrect
spacing for what should be treated as a variable, and also incorrect
vertical position of the base. Perhaps amsmath.sty with
\vec{\vec{\epsilon}?
Yes, that is better.
Paul Wagner
2004-10-22 11:13:27 UTC
Permalink
Post by mrlinux
Hi,
How can I get the tensor symbol, I mean the doublearrow over \epsilon ???
thanks in advance
Hi,

the \stackrel business is a possibility, but compared to a \vec it looks
different, simply because the arrow is much larger in size. As far is I
know, there is no double arrow accent in TeX (CM fonts, to be precise), but
I assume it would be easy to write a new meta-font glyph based on the \vec
accent.

Paul
Paul Kornman
2004-10-23 01:57:38 UTC
Permalink
Post by Paul Wagner
Post by mrlinux
Hi,
How can I get the tensor symbol, I mean the doublearrow over \epsilon ???
thanks in advance
Hi,
the \stackrel business is a possibility, but compared to a \vec it
looks different, simply because the arrow is much larger in size. As
far is I know, there is no double arrow accent in TeX (CM fonts, to be
precise), but I assume it would be easy to write a new meta-font glyph
based on the \vec accent.
Paul
As I recall (approx. 20 yrs. ago) this was used in physics -
particularll (from what I remember) in Arfkin's (sp?) math methods
book, Goldstein's dynamics and J. D. Jackson's Electrodynamics. From
what I've seen in the recent literature, the other posters seem correct.
Madhusudan Singh
2004-10-23 06:16:33 UTC
Permalink
Post by Paul Kornman
As I recall (approx. 20 yrs. ago) this was used in physics -
particularll (from what I remember) in Arfkin's (sp?) math methods
G. Arfken.
Post by Paul Kornman
book, Goldstein's dynamics and J. D. Jackson's Electrodynamics. From
what I've seen in the recent literature, the other posters seem correct.
Good books all.
ABKaye
2004-10-23 02:22:09 UTC
Permalink
Post by mrlinux
Hi,
How can I get the tensor symbol, I mean the doublearrow over \epsilon ???
thanks in advance
The double-arrow convention isn't new, but most texts use bold capital
letters for tensors (with or without their indicies, depending upon the
usage), italic letters with arrows for vectors, and italic letters without
additional notation for scalars.

I have not seen the double-arrow symbol in a latex document, but that
doesn't mean it doesn't exist.
Abhishek Agrawal
2004-10-23 09:39:23 UTC
Permalink
have you checked tensor.sty ( i have not but it may be what you are looking for)
-abhishek
ABKaye
2004-10-24 20:31:04 UTC
Permalink
\leftrightarrow seems to work OK. I found it in the "comprehensive"
list of latex symbols.
mrlinux
2004-10-25 14:57:57 UTC
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Post by ABKaye
\leftrightarrow seems to work OK. I found it in the "comprehensive"
list of latex symbols.
yes I found it but I didn't know about \stackrel{} ... so I solved my
problem thank you.

Actually this notation is rather old but used in some papers
(phisics/optics) and to say the truth I don't like it very much; maybe
I'll change the tensor symbol symply writing \epsilon with a bold
font (other used convention).


Thank you to all

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